Fast Convolution for Nonreflecting Boundary Conditions
From MaRDI portal
Publication:4785916
DOI10.1137/S1064827501388741zbMath1013.65113MaRDI QIDQ4785916
Christian Lubich, Achim Schädle
Publication date: 5 January 2003
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
algorithmwave equationnumerical examplesboundary element methodSchrödinger equationtransparent boundary conditionsLaplace transform methodradiation boundary conditionsnonreflecting boundary conditionsconvolution integralsfast convolution algorithmFourier or spherical expansions
Wave equation (35L05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
Related Items
A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS, An efficient and fast parallel method for Volterra integral equations of Abel type, A self-singularity-capturing scheme for fractional differential equations, A fast and oblivious matrix compression algorithm for Volterra integral operators, A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions, Numerical solution of multi-term time fractional wave diffusion equation using transform based local meshless method and quadrature, Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation, A stable fast time-stepping method for fractional integral and derivative operators, Exponential-sum-approximation technique for variable-order time-fractional diffusion equations, Nonreflecting boundary conditions for discrete waves, Open boundaries for the nonlinear Schrödinger equation, Absorbing boundary conditions for nonlinear scalar partial differential equations, Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions, A bootstrap method for sum-of-poles approximations, A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system, A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D, High order full discretizations of coupled wave equations with absorbing boundary conditions and geometric integration, Stability and Error Analysis for a Second-Order Fast Approximation of the One-dimensional Schrödinger Equation Under Absorbing Boundary Conditions, Perfectly matched layers versus discrete transparent boundary conditions in quantum device simulations, Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain, Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory, Nonreflecting boundary condition for time-dependent multiple scattering, Nonreflecting boundary conditions for the time-dependent convective wave equation in a duct, Exact non-reflecting boundary conditions revisited: well-posedness and stability, Numerical solution of coupled nonlinear Schrödinger equations on unbounded domains, Space reduction for linear systems with local symmetry, Stochastic P-Bifurcation Analysis of Fractional Smooth and Discontinuous Oscillator with an Extended Fast Method, Optimized overlapping Schwarz waveform relaxation for a class of time-fractional diffusion problems, Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations, Fast and efficient finite difference method for the distributed-order diffusion equation based on the staggered grids, High-order accurate adaptive kernel compression time-stepping schemes for fractional differential equations, A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications, Fast difference scheme for a tempered fractional Burgers equation in porous media, A variably distributed-order time-fractional diffusion equation: analysis and approximation, A kernel-independent sum-of-exponentials method, Implicit-explicit time integration of nonlinear fractional differential equations, Time-dependent simulations of quantum waveguides using a time-splitting spectral method, Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms, A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations, The numerical computation of the time fractional Schrödinger equation on an unbounded domain, A fast algorithm for multilinear operators, A Kernel Compression Scheme for Fractional Differential Equations, Talbot quadratures and rational approximations, Fast \(\theta\)-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis, Efficient high order algorithms for fractional integrals and fractional differential equations, The singularity method in unsteady Stokes flow: hydrodynamic force and torque around a sphere in time-dependent flows, Numerical approximation of the Schrödinger equation with concentrated potential, An exact non reflecting boundary condition for 2D time-dependent wave equation problems, Fast and Parallel Runge--Kutta Approximation of Fractional Evolution Equations, Legendre spectral methods based on two families of novel second-order numerical formulas for the fractional activator-inhibitor system, Multiscale resolution of shortwave‐longwave interaction, An Efficient Second-Order Finite Difference Method for the One-Dimensional Schrödinger Equation with Absorbing Boundary Conditions, Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain, Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line, A perfectly matched layer approach to the nonlinear Schrödinger wave equations, A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums, Time-domain implementation of nonreflecting boundary-conditions for the nonlinear Euler equations, A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics, Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations, Implementation of nonreflecting boundary conditions for the nonlinear Euler equations, A Gauss-Jacobi kernel compression scheme for fractional differential equations, Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip, Nonreflecting boundary conditions for the time-dependent wave equation, Local nonreflecting boundary condition for time-dependent multiple scattering, Efficient long-time computations of time-domain boundary integrals for 2D and dissipative wave equation, Fast evaluation of nonreflecting boundary conditions for the Schrödinger equation in one dimension, The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions, Fast and stable evaluation of the exact absorbing boundary condition for the semi-discrete linear Schrödinger equation in unbounded domains, Radiation boundary conditions for time-dependent waves based on complete plane wave expansions, Stable numerical coupling of exterior and interior problems for the wave equation, A thermodynamically consistent fractional visco-elasto-plastic model with memory-dependent damage for anomalous materials, Fast collocation methods for Volterra integral equations of convolution type, A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations, A method of boundary equations for unsteady hyperbolic problems in 3D, The partial fast Fourier transform, Fast Runge-Kutta methods for nonlinear convolution systems of Volterra integral equations, Transparent boundary condition for numerical modeling of intense laser-molecule interaction, Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations, Dynamics of steps along a martensitic phase boundary. II: Numerical simulations, Discrete absorbing boundary conditions for Schrödinger-type equations. Practical implementation, OPTIMIZED AND QUASI-OPTIMAL SCHWARZ WAVEFORM RELAXATION FOR THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION, Near-field infinity-simulating boundary conditions for the heat equation, Convolution quadrature time discretization of fractional diffusion-wave equations, Fast Evaluation of Artificial Boundary Conditions for Advection Diffusion Equations, Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data, An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative, Fractional-order uniaxial visco-elasto-plastic models for structural analysis, Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time, Fast difference scheme for the reaction-diffusion-advection equation with exact artificial boundary conditions, A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes, Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain, Incomplete iterative solution of subdiffusion, Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation, Diffusive realizations for solutions of some operator equations: The one-dimensional case, Local absorbing boundaries of elliptical shape for scalar waves, Analysis of a backward Euler-type scheme for Maxwell’s equations in a Havriliak–Negami dispersive medium, Fast Runge-Kutta approximation of inhomogeneous parabolic equations, A fast, high-order numerical method for the simulation of single-excitation states in quantum optics, On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations, Efficient sum-of-exponentials approximations for the heat kernel and their applications, Fast and Oblivious Algorithms for Dissipative and Two-dimensional Wave Equations, A fast time-stepping method based on the \(hp\)-version spectral collocation method for the nonlinear fractional delay differential equation, One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity, Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation, A corrected \(\mathrm{L}1\) method for a time-fractional subdiffusion equation, A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions, A fast accurate artificial boundary condition for the Euler-Bernoulli beam, Unconditionally convergent numerical method for the fractional activator–inhibitor system with anomalous diffusion, Long time \(H^1\)-stability of fast \(\mathrm{L}2\)-\(1_\sigma\) method on general nonuniform meshes for subdiffusion equations, Enhanced parallel computation for time-fractional fluid dynamics: a fast time-stepping method with Newton-Krylov-Schwarz solver, Fast artificial boundary method for the heat equation on unbounded domains with strip tails, A fast time domain solver for the equilibrium Dyson equation, A Sparse Reformulation of the Green’s Function Formalism Allows Efficient Simulations of Morphological Neuron Models, Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme, Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain, Fast One-Dimensional Convolution with General Kernels Using Sum-of-Exponential Approximation, Convergence Analysis of Schwarz Waveform Relaxation with Convolution Transmission Conditions, Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations, Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations
